Kinematics of motion in a straight line: past paper questions

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• Question 3May/June 2026, paper 41Structured8 marks

  A particle $P$ travels in a straight line, starting from a point $O$. At time $t$ seconds the displacement of $P$ from $O$ is $s$ metres, where $s=4t^3-39t^2+120t$. Find the values of $t$ for which $P$ is instantaneously at rest.

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• Question 6Oct/Nov 2025, paper 41Structured6 marks

  A particle $A$ of mass $2.5\text{ kg}$ is released from rest from the top of a smooth plane, which makes an angle of ${\sin }^{-1}0.2$ with the horizontal.

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• Question 4Oct/Nov 2024, paper 41Structured6 marks

  A bus travels between two stops, $A$ and $B$. The bus starts from rest at $A$ and accelerates at a constant rate of $a{\text{ ms}}^{-2}$ until it reaches a speed of $16{\text{ ms}}^{-1}$.

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• Question 3Oct/Nov 2023, paper 41Structured8 marksHas a diagram

  The diagram shows the velocity-time graph for the motion of a bus. The bus starts from rest and accelerates uniformly for $8\text{ seconds}$ until it reaches a speed of $12.6{\text{ m s}}^{-1}$. The bus maintains this speed for $40\text{ seconds}$.

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• Question 4May/June 2026, paper 41Structured10 marks

  Three particles $A$, $B$ and $C$ have masses $3\text{ kg}$, $1.5\text{ kg}$ and $m\text{ kg}$ respectively, where $m>1.5$. Particles $A$ and $B$ are attached to the ends of a light inextensible string that passes over a smooth fixed pulley.

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• Question 7Oct/Nov 2025, paper 41Structured9 marks

  A particle $P$ starts from a point $O$ and moves in a straight line. The velocity $v{\text{ ms}}^{-1}$ of $P$, at time $t\text{ s}$ after leaving $O$, is given by $v=\frac{1}{3}(2t-3)(t-4)$. Find the acceleration of $P$ when $t=2$.

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• Question 5Oct/Nov 2024, paper 41Structured10 marks

  A particle, $A$, is projected vertically upwards from a point $O$ with a speed of $80{\text{ ms}}^{-1}$. One second later a second particle, $B$, with the same mass as $A$, is projected vertically upwards from $O$ with a speed of $100{\text{ ms}}^{-1}$.

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• Question 7Oct/Nov 2023, paper 41Structured9 marks

  A particle moves in a straight line starting from a point $O$ before coming to instantaneous rest at a point $X$.

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• Question 2May/June 2026, paper 42Structured4 marks

  Two particles, $A$ and $B$, of masses $2.5\text{ kg}$ and $3.5\text{ kg}$ respectively are at rest on a straight smooth horizontal track. Particle $B$ is situated $9\text{ m}$ from a vertical wall which is fixed at right angles to the track.

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• Question 1Oct/Nov 2025, paper 42Structured3 marksHas a diagram

  The diagram shows the displacement-time graph for the motion of a particle. The particle starts from rest at a point $O$ and travels with constant acceleration $a\text{ m}{\text{ s}}^{-2}$, taking $4\text{ s}$ to move a distance of $x\text{ m}$.

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• Question 8Oct/Nov 2024, paper 41Structured7 marks

  A particle $P$ moves in a straight line, passing through a point $O$ with velocity $4.2{\text{ ms}}^{-1}$. At time $t\text{ s}$ after $P$ passes $O$, the acceleration, $a{\text{ ms}}^{-2}$, of $P$ is given by $a=0.6t-2.7$.

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• Question 4Oct/Nov 2023, paper 42Structured7 marks

  A particle $P$ of mass $0.2\text{ kg}$ lies at rest on a rough horizontal plane. A horizontal force of $1.2\text{ N}$ is applied to $P$. Given that $P$ is in limiting equilibrium, find the coefficient of friction between $P$ and the plane.

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• Question 4May/June 2026, paper 42Structured9 marksHas a diagram

  A particle $P$ is projected from a point $A$ with speed $4{\text{ ms}}^{-1}$ up a line of greatest slope of a rough plane inclined at an angle $\theta$ to the horizontal, where $\tan \theta =\frac{4}{3}$. $P$ comes to instantaneous rest at a point $B$ on the plane (see diagram).

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• Question 3Oct/Nov 2025, paper 42Structured8 marks

  A car of mass $1400\text{ kg}$ travelling on a straight horizontal road accelerates uniformly from a speed of $15\text{ m}{\text{ s}}^{-1}$ to $20\text{ m}{\text{ s}}^{-1}$ over a distance of $175\text{ m}$. Find the time taken to travel the $175\text{ m}$.

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• Question 1Oct/Nov 2024, paper 42Structured5 marks

  The velocity of a particle moving in a straight line at time $t$ seconds after leaving a fixed point $O$ is $v{\mathrm{m}\mathrm{s}}^{-1}$. The diagram shows a velocity-time graph which models the motion of the particle from $t=0$ to $t=T$.

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• Question 5Oct/Nov 2023, paper 42Structured8 marks

  A particle $A$ of mass $0.5\text{ kg}$ is projected vertically upwards from horizontal ground with speed $25\text{ m}{\text{ s}}^{-1}$. Find the speed of $A$ when it reaches a height of $20\text{ m}$ above the ground.

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• Question 5May/June 2026, paper 42Structured6 marks

  The points $A$ and $B$ are at the same vertical height $h\text{ m}$ above horizontal ground. A particle $P$ is released from rest from $A$. One second later, a particle $Q$ is projected vertically downwards from $B$ with speed $18{\text{ ms}}^{-1}$.

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• Question 4Oct/Nov 2025, paper 42Structured9 marks

  A particle $P$ of mass $0.1\text{ kg}$ is projected vertically upwards with speed $30\text{ m}{\text{ s}}^{-1}$ from horizontal ground.

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• Question 5Oct/Nov 2024, paper 42Structured9 marks

  Two particles, $P$ and $Q$, of masses $2m\mathrm{k}\mathrm{g}$ and $m\mathrm{k}\mathrm{g}$ respectively, are held at rest in the same vertical line. The heights of $P$ and $Q$ above horizontal ground are $1\mathrm{m}$ and $2\mathrm{m}$ respectively.

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• Question 7Oct/Nov 2023, paper 42Structured12 marks

  A particle $X$ travels in a straight line. The velocity of $X$ at time $t\text{ s}$ after leaving a fixed point $O$ is denoted by $v\text{ m}{\text{ s}}^{-1}$, where $$v=-0.1t^3+1.8t^2-6t+\mathrm{5.6.}$$ The acceleration of $X$ is zero at $t=p$ and $t=q$, where $p<q$.

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• Question 6May/June 2026, paper 42Structured8 marksHas a diagram

  A crate of weight $W\text{ N}$ is at rest on rough horizontal ground. The crate is pulled at a constant acceleration of $1.5{\text{ ms}}^{-2}$ along the ground in a straight line by a light rope.

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• Question 6Oct/Nov 2024, paper 42Structured10 marks

  A particle, $P$, travels in a straight line, starting from a point $O$ with velocity $6{\mathrm{m}\mathrm{s}}^{-1}$.

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• Question 1Oct/Nov 2023, paper 43Structured3 marks

  A particle is projected vertically upwards from horizontal ground with a speed of $u\text{ m}{\text{ s}}^{-1}$. The particle has height $s\text{ m}$ above the ground at times 3 seconds and 4 seconds after projection. Find the value of $u$ and the value of $s$.

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• Question 7May/June 2026, paper 42Structured9 marks

  A particle $P$ moves in a straight line.

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• Question 1Oct/Nov 2025, paper 43Structured3 marksHas a diagram

  The diagram shows the velocity-time graph for the motion of an athlete. The athlete runs in a straight line from point $A$ to point $B$, runs back to point $A$ and finishes at point $B$. The graph consists of four straight line segments.

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• Question 7Oct/Nov 2024, paper 42Structured11 marksHas a diagram

  Two particles, $A$ and $B$, of masses $0.2\mathrm{k}\mathrm{g}$ and $0.3\mathrm{k}\mathrm{g}$ respectively, are attached to the ends of a light inextensible string.

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• Question 3Oct/Nov 2023, paper 43Structured6 marks

  A block of mass $8\text{ kg}$ slides down a rough plane inclined at ${30}^{\circ }$ to the horizontal, starting from rest. The coefficient of friction between the block and the plane is $\mu$. The block accelerates uniformly down the plane at $2.4\text{ m}{\text{ s}}^{-2}$.

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• Question 1May/June 2026, paper 43Structured4 marks

  A particle is projected vertically upwards with speed $u{\mathrm{m}\mathrm{s}}^{-1}$ from a point on horizontal ground. The height of the particle above the ground after 4 seconds is equal to its height above the ground after 6 seconds. Find the value of $u$.

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• Question 4Oct/Nov 2025, paper 43Structured10 marks

  A particle $P$ moves in a straight line. At time $t\text{ s}$ after passing through a point $O$ on the line, the displacement of $P$ from $O$ is $s\text{ m}$, where $s=0.01t^3-0.3t^2-2.07t$.

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• Question 6Oct/Nov 2024, paper 43Structured10 marks

  A particle moves in a straight line. It starts from rest, at time $t=0$, and accelerates at $0.6t\text{ m}{\text{s}}^{-2}$ for $4\text{ s}$, reaching a speed of $V\text{ m}{\text{s}}^{-1}$.

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